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Happy √2²²-22 -- And other ways to calculate 2026

Ed Pegg, Wolfram Research
Posted 2 months ago 
√2^22-22   == 2026    
12/3!×4^5+67-89 == 2026    
123/4!×56×7+8+9  == 2026   
12×34×5-6-7+8-9  == 2026      
987+65×4!/3×2-1 == 2026   
9!/8/7/6+5^4+321 == 2026  
9×8-7+654×3-2+1 == 2026  
9+8×7+654×3-2+1 == 2026  
987+6!+5×4^3-2+1 == 2026  
1+2+345×6-7×8+9 == 2026   
9×8+76+5^4×3+2+1 == 2026   
⌈Cosh[9]/2⌉   == 2026

Also, if you want a single denominator to make fractions in between all the values of FareySequence[52], the smallest denominator you can use is 2026. 

Sort[Join[
  Union[Round[2026 Mean[#]] & /@ Partition[FareySequence[52], 2, 1]]/
   2026 , FareySequence[52]]]

There's also: 

FromContinuedFraction[{45, {90}}]

And so long to 2025. Using Ponting Square Packing, here are all the squares with edge 1 to 2025 in one big blob.

enter image description here
POSTED BY: Ed Pegg
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POSTED BY: Bert Sierra

Here are the ones I found using the code in the attached notebook (the ones with "✓" are in the original post):

{
 1 + 2*3/4/5/6*7!*8 + 9,
 1 + 2 + 3*4! + 5/6!*7*8! - 9,
 1 + 2 + 345*6 - 7*8 + 9,(*✓*)
 1 - 2*3!*456*7 + 8! + 9,
 12/3!*4^5 + 67 - 89,
 12^3 + 45/6!*7! - 8 - 9,
 123/4!*56*7 + 8 + 9  (*✓*)
}

(*{2026, 2026, 2026, 2026, 2026, 2026, 2026}*)

Full code below and notebook attached at the end:

Attachments:
Hunt-for-express...nb
POSTED BY: Anton Antonov
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